Exactly! There absolutely has to be some sort of verified and
solid evidence in hand before the police can proceed.

A phone call or email is never enough by itself, so the police
have to investigate and get some probable cause that a
crime has been committed before getting a warrant for
search or arrest. Someone who has accidentally
downloaded and then deleted a file is never going to find
themselves in such a position because no such evidence
exists. Any search or arrest (which would have to be based
solely on hearsay or suspicion) against such a person would
automatically be thrown out of court as soon as it is
discovered that the mandatory hurdle of probable cause had
been ignored.

Even if a person had been caught with millions of files, that
evidence would be permanently inadmissible if the police
had obtained it illegally. In the case where an innocent
person is illegally tagged with a single file, it would be the
policemen and prosecutors facing criminal charges, not the
other way around.

What you are describing there is a case involving a person
who shares such files, against whom a screenshot
showing the files being shared can be obtained. If
you are imagining a case in which an innocent person could
be logged downloading such a file, don't forget that
the only person capable of providing a screenshot or
testimony is the very same person who is actually
sharing the file and breaking the law. The police
cannot ever commit a crime to catch a criminal, so that
scenario is completely ruled out too.

The bottom line is that anyone who accidentally downloads
and then deletes an illegal file of any kind is completely
safe from prosecution. The only way they could get
themselves in trouble is to let themselves be tricked into
confessing to more than they actually did. Even then, any
competent lawyer could expose the trickery and nullify that
improbable and hypothetical threat.

So, there's not much point in destroying all your data and
reformatting your whole disk when just deleting the file and
defragging or wiping free space is going to work well
enough. In fact, taking such an extreme measure will tend
to indicate to anybody that more was going on and would
tend to raise suspicion.